Applied Statistics and Probability for Engineers
4-2 PROBABILITY DISTRIBUTIONS AND PROBABILITY DENSITY FUNCTIONS 99 under the density function over this interval, and it can be ...
100 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS the same function, f(x), over the smaller interval. By a ...
4-2 PROBABILITY DISTRIBUTIONS AND PROBABILITY DENSITY FUNCTIONS 101 As another example, EXAMPLE 4-2 Let the continuous random va ...
Extending the definition of f(x) to the entire real line enables us to define the cumulative dis- tribution function for all rea ...
4-3 CUMULATIVE DISTRIBUTION FUNCTIONS 103 and Finally, Therefore, The plot of F(x) is shown in Fig. 4-6. Notice that in the defi ...
104 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS The probability density function of a continuous random ...
4-4 MEAN AND VARIANCE OF A CONTINUOUS RANDOM VARIABLE The mean and variance of a continuous random variable are defined similarl ...
106 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS EXAMPLE 4-7 In Example 4-1, Xis the current measured in ...
4-5 CONTINUOUS UNIFORM DISTRIBUTION The simplest continuous distribution is analogous to its discrete counterpart. 4-5 CONTINUOU ...
108 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS EXAMPLE 4-9 Let the continuous random variable Xdenote t ...
4-6 NORMAL DISTRIBUTION 109 4-6 NORMAL DISTRIBUTION Undoubtedly, the most widely used model for the distribution of a random var ...
110 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Figure 4-10 Normal probability density functions for sel ...
4-6 NORMAL DISTRIBUTION 111 probability density function decreases as xmoves farther from. Consequently, the probability that a ...
112 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Probabilities that are not of the form P(Zz) are found ...
(5) cannot be found exactly from Appendix Table II. However, the last entry in the table can be used to find that. Because is ne ...
114 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Figure 4-15 Standardizing a normal random variable. 4 7 ...
Therefore, (x10) 2 2.05, and the standardizing transformation is used in reverse to solve for x. The result is EXAMPLE 4-15 A ...
116 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Therefore, and Suppose a digital 1 is represented as a s ...
4-6 NORMAL DISTRIBUTION 117 Mean and Variance of the Normal Distribution (CD Only) EXERCISES FOR SECTION 4-6 4-39. Use Appendix ...
118 CHAPTER 4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 4-53. The reaction time of a driver to visual stimulus i ...
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